If you lose a good fish and have a curl on the end of the line, you probably just had a bad knot. You can avoid many of those "break offs" with a good knot. I use a palomar knot in most cases. It is extremely strong because the line is wrapped around the eye twice. About the only time I don't use a palomar with mono or braid is when I have a bait (such as a Pop-R) that either is hard to put a double line through or I think it may have better action if it isn't doubled. In that case, I use the clinch knot.
To tie a palomar knot, double (fold) your line and put it through the eye of your lure. Then take the folded end and go over and back under the other lines and grab the folded end. Now, put your lure completely through the loop you just made. Then pull the tag end of the line to take out the excess. Now hold the lure and pull the line to tighten it. Cut off the excess and you should have a good palomar knot. I believe this is the strongest knot for braided line and monofilament line. It takes me about 2 seconds to tie this knot, which is one reason it is a favorite.
I recommend a Trilene knot for fluorocarbon. To tie a Trilene knot, put your line through the eye, form a circle with it and put it through the eye again. You leave enough excess line that you can wrap the excess around the line and tag 5 times. After wrapping 5 times, you put the tag end through the circle you made. Then, you wet it and clinch it. This is the strongest knot for flourocarbon line.
Improved Clinch Knot
To tie a clinch knot, put your line through the eye of your lure and leave about 6 inches. Hold both lines together and twist your lure 5 or 6 full turns. Put the excess line through the loop close to your bait, then put it back through the loop you just made. Pull on the excess while pushing the knot toward the bait. Now hold the lure and pull the line to tighten it. Cut off the excess and you should have a good clinch knot.
I believe the Alberto Knot is the best for tying braid to fluorocarbon. It may be easier to learn by watching a video. You can find several on the Internet. I'll try to make one when I get around to it.